Details

analyze1.9s (27.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
1.1%	98.6%	0.3%	12
1.9%	97.8%	0.3%	13
7%	92.7%	0.3%	14

Compiler

Compiled 28 to 17 computations (39.3% saved)

sample33.0ms (0.5%)

Algorithm

1×

intervals

Results

21.0ms

256×

body

128

valid

Compiler

Compiled 61 to 39 computations (36.1% saved)

simplify94.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

765×	`sub-neg_binary64`
731×	`fma-neg_binary64`
652×	`neg-mul-1_binary64`
505×	`fma-def_binary64`
495×	`cancel-sign-sub-inv_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	29
1	37	29
2	85	29
3	194	27
4	486	27
5	1003	27
6	1920	27
7	3406	27
8	4078	27
9	4431	27
10	4919	27
11	5085	27

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

28.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	28.7b	(/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))

Compiler

Compiled 96 to 51 computations (46.9% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(fma.f64 (+.f64 x y) z (*.f64 t a))
✓	2.0b	(fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))
✓	26.9b	(/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))

series182.0ms (2.6%)

Counts

3 → 204

Calls

3 calls:

143.0ms	(/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))
25.0ms	(fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))
13.0ms	(fma.f64 (+.f64 x y) z (*.f64 t a))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64`
15×	`times-frac_binary64`
13×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
12×	`distribute-lft-out_binary64`

Counts

3 → 59

Calls

3 calls:

8.0ms	(/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))
0.0ms	(fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a)))
0.0ms	(fma.f64 (+.f64 x y) z (*.f64 t a))

simplify157.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

591×	`associate-/l*_binary64`
378×	`associate-/r*_binary64`
286×	`+-commutative_binary64`
241×	`associate-+r+_binary64`
237×	`associate--l+_binary64`

Counts

263 → 200

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	673	11356
1	1961	11106
2	5078	11106

prune174.0ms (2.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	186	14	200
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	187	14	201

Error

2.6b

Counts

201 → 14

Alt Table

Status	Error	Program
	50.7b	(.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 y t) 3))) (+.f64 (.f64 x x) (-.f64 (.f64 (+.f64 y t) (+.f64 y t)) (*.f64 x (+.f64 y t)))))
	44.3b	z
	29.3b	(/.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (.f64 (cbrt.f64 (+.f64 x (+.f64 y t))) (cbrt.f64 (+.f64 x (+.f64 y t))))) (cbrt.f64 (+.f64 x (+.f64 y t))))
	29.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (.f64 a t)))) (cbrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (.f64 a t))))) (/.f64 (cbrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t)))) (+.f64 (+.f64 t x) y)))
	45.5b	(.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (.f64 a t))) (-.f64 (*.f64 x x) (pow.f64 (+.f64 t y) 2))) (-.f64 x (+.f64 y t)))
	45.6b	(.f64 (sqrt.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (+.f64 x (+.f64 y t)))) (sqrt.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))))
	42.0b	(/.f64 (fma.f64 a t (*.f64 z x)) (+.f64 t x))
	44.7b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t))) (+.f64 (+.f64 t x) y)) 3))
▶	28.4b	(-.f64 (+.f64 a z) b)
	53.2b	(neg.f64 (/.f64 (*.f64 y b) (+.f64 (+.f64 t x) y)))
	28.7b	(/.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t))) (+.f64 x (+.f64 y t)))
	46.1b	(-.f64 (+.f64 (/.f64 (.f64 y a) t) (+.f64 a (+.f64 (/.f64 (.f64 z x) t) (/.f64 (.f64 y z) t)))) (+.f64 (/.f64 (.f64 a x) t) (+.f64 (/.f64 (.f64 a y) t) (/.f64 (.f64 y b) t))))
	43.0b	a
	44.6b	(*.f64 (/.f64 z (+.f64 (+.f64 t x) y)) (+.f64 x y))

Compiler

Compiled 10845 to 3255 computations (70% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 a z) b)

series5.0ms (0.1%)

Counts

1 → 9

Calls

1 calls:

5.0ms

(-.f64 (+.f64 a z) b)

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`prod-diff_binary64`
10×	`add-cube-cbrt_binary64`
6×	`add-log-exp_binary64`

Counts

1 → 37

Calls

1 calls:

5.0ms

(-.f64 (+.f64 a z) b)

simplify74.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

886×	`times-frac_binary64`
653×	`associate-+l+_binary64`
560×	`fma-neg_binary64`
391×	`*-commutative_binary64`
293×	`associate-l_binary64`

Counts

46 → 51

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	71	676
1	135	385
2	446	346
3	1951	345
4	3407	345
5	4746	345
6	5579	345

prune47.0ms (0.7%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	46	5	51
Fresh	1	12	13
Picked	1	0	1
Done	0	0	0
Total	48	17	65

Error

2.6b

Counts

65 → 17

Alt Table

Status	Error	Program
▶	28.4b	(+.f64 a (-.f64 z b))
	50.7b	(.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 y t) 3))) (+.f64 (.f64 x x) (-.f64 (.f64 (+.f64 y t) (+.f64 y t)) (*.f64 x (+.f64 y t)))))
	44.3b	z
	40.9b	(-.f64 z b)
	53.2b	(neg.f64 (/.f64 (*.f64 y b) (+.f64 (+.f64 t x) y)))
	29.3b	(/.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (.f64 (cbrt.f64 (+.f64 x (+.f64 y t))) (cbrt.f64 (+.f64 x (+.f64 y t))))) (cbrt.f64 (+.f64 x (+.f64 y t))))
	29.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (.f64 a t)))) (cbrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (.f64 a t))))) (/.f64 (cbrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t)))) (+.f64 (+.f64 t x) y)))
	30.7b	(+.f64 a z)
	45.5b	(.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (.f64 a t))) (-.f64 (*.f64 x x) (pow.f64 (+.f64 t y) 2))) (-.f64 x (+.f64 y t)))
	45.6b	(.f64 (sqrt.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (+.f64 x (+.f64 y t)))) (sqrt.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))))
	42.0b	(/.f64 (fma.f64 a t (*.f64 z x)) (+.f64 t x))
	44.7b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t))) (+.f64 (+.f64 t x) y)) 3))
	44.2b	(expm1.f64 (log1p.f64 (-.f64 (+.f64 a z) b)))
	29.1b	(.f64 (.f64 (cbrt.f64 (-.f64 (+.f64 a z) b)) (cbrt.f64 (-.f64 (+.f64 a z) b))) (cbrt.f64 (-.f64 (+.f64 a z) b)))
	28.7b	(/.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t))) (+.f64 x (+.f64 y t)))
	46.1b	(-.f64 (+.f64 (/.f64 (.f64 y a) t) (+.f64 a (+.f64 (/.f64 (.f64 z x) t) (/.f64 (.f64 y z) t)))) (+.f64 (/.f64 (.f64 a x) t) (+.f64 (/.f64 (.f64 a y) t) (/.f64 (.f64 y b) t))))
	44.6b	(*.f64 (/.f64 z (+.f64 (+.f64 t x) y)) (+.f64 x y))

Compiler

Compiled 1551 to 630 computations (59.4% saved)

localize3.0ms (0.1%)

prune18.0ms (0.3%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	16	16
Picked	1	1
Done	0	0
Total	17	17

Error

2.6b

Counts

17 → 17

Alt Table

Status	Error	Program
✓	28.4b	(+.f64 a (-.f64 z b))
	50.7b	(.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 y t) 3))) (+.f64 (.f64 x x) (-.f64 (.f64 (+.f64 y t) (+.f64 y t)) (*.f64 x (+.f64 y t)))))
	44.3b	z
	40.9b	(-.f64 z b)
	53.2b	(neg.f64 (/.f64 (*.f64 y b) (+.f64 (+.f64 t x) y)))
	29.3b	(/.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (.f64 (cbrt.f64 (+.f64 x (+.f64 y t))) (cbrt.f64 (+.f64 x (+.f64 y t))))) (cbrt.f64 (+.f64 x (+.f64 y t))))
	29.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (.f64 a t)))) (cbrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (.f64 a t))))) (/.f64 (cbrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t)))) (+.f64 (+.f64 t x) y)))
	30.7b	(+.f64 a z)
	45.5b	(.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (.f64 a t))) (-.f64 (*.f64 x x) (pow.f64 (+.f64 t y) 2))) (-.f64 x (+.f64 y t)))
	45.6b	(.f64 (sqrt.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (+.f64 x (+.f64 y t)))) (sqrt.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))))
	42.0b	(/.f64 (fma.f64 a t (*.f64 z x)) (+.f64 t x))
	44.7b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t))) (+.f64 (+.f64 t x) y)) 3))
	44.2b	(expm1.f64 (log1p.f64 (-.f64 (+.f64 a z) b)))
	29.1b	(.f64 (.f64 (cbrt.f64 (-.f64 (+.f64 a z) b)) (cbrt.f64 (-.f64 (+.f64 a z) b))) (cbrt.f64 (-.f64 (+.f64 a z) b)))
▶	28.7b	(/.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t))) (+.f64 x (+.f64 y t)))
	46.1b	(-.f64 (+.f64 (/.f64 (.f64 y a) t) (+.f64 a (+.f64 (/.f64 (.f64 z x) t) (/.f64 (.f64 y z) t)))) (+.f64 (/.f64 (.f64 a x) t) (+.f64 (/.f64 (.f64 a y) t) (/.f64 (.f64 y b) t))))
	44.6b	(*.f64 (/.f64 z (+.f64 (+.f64 t x) y)) (+.f64 x y))

Compiler

Compiled 879 to 452 computations (48.6% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(fma.f64 z (+.f64 x y) (*.f64 a t))
✓	2.0b	(fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t)))
✓	26.9b	(/.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t))) (+.f64 x (+.f64 y t)))

series186.0ms (2.7%)

Counts

3 → 204

Calls

3 calls:

145.0ms	(/.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t))) (+.f64 x (+.f64 y t)))
27.0ms	(fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t)))
14.0ms	(fma.f64 z (+.f64 x y) (*.f64 a t))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64`
15×	`times-frac_binary64`
13×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
12×	`distribute-lft-out_binary64`

Counts

3 → 59

Calls

3 calls:

5.0ms	(/.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t))) (+.f64 x (+.f64 y t)))
0.0ms	(fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t)))
0.0ms	(fma.f64 z (+.f64 x y) (*.f64 a t))

simplify155.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

591×	`associate-/l*_binary64`
378×	`associate-/r*_binary64`
286×	`+-commutative_binary64`
241×	`associate-+r+_binary64`
237×	`associate--l+_binary64`

Counts

263 → 187

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	672	11356
1	1961	11106
2	5078	11106

prune136.0ms (2%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	186	1	187
Fresh	1	14	15
Picked	0	1	1
Done	0	1	1
Total	187	17	204

Error

2.6b

Counts

204 → 17

Alt Table

Status	Error	Program
✓	28.4b	(+.f64 a (-.f64 z b))
	50.7b	(.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 y t) 3))) (+.f64 (.f64 x x) (-.f64 (.f64 (+.f64 y t) (+.f64 y t)) (*.f64 x (+.f64 y t)))))
	40.9b	(-.f64 z b)
	53.2b	(neg.f64 (/.f64 (*.f64 y b) (+.f64 (+.f64 t x) y)))
	29.3b	(/.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (.f64 (cbrt.f64 (+.f64 x (+.f64 y t))) (cbrt.f64 (+.f64 x (+.f64 y t))))) (cbrt.f64 (+.f64 x (+.f64 y t))))
	29.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (.f64 a t)))) (cbrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (.f64 a t))))) (/.f64 (cbrt.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t)))) (+.f64 (+.f64 t x) y)))
	30.7b	(+.f64 a z)
	45.5b	(.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (.f64 a t))) (-.f64 (*.f64 x x) (pow.f64 (+.f64 t y) 2))) (-.f64 x (+.f64 y t)))
	45.6b	(.f64 (sqrt.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (.f64 t a))) (+.f64 x (+.f64 y t)))) (sqrt.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 (+.f64 x y) z (*.f64 t a))) (+.f64 x (+.f64 y t)))))
	42.0b	(/.f64 (fma.f64 a t (*.f64 z x)) (+.f64 t x))
	44.7b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t))) (+.f64 (+.f64 t x) y)) 3))
	44.2b	(expm1.f64 (log1p.f64 (-.f64 (+.f64 a z) b)))
	29.1b	(.f64 (.f64 (cbrt.f64 (-.f64 (+.f64 a z) b)) (cbrt.f64 (-.f64 (+.f64 a z) b))) (cbrt.f64 (-.f64 (+.f64 a z) b)))
✓	28.7b	(/.f64 (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t))) (+.f64 x (+.f64 y t)))
	46.1b	(-.f64 (+.f64 (/.f64 (.f64 y a) t) (+.f64 a (+.f64 (/.f64 (.f64 z x) t) (/.f64 (.f64 y z) t)))) (+.f64 (/.f64 (.f64 a x) t) (+.f64 (/.f64 (.f64 a y) t) (/.f64 (.f64 y b) t))))
	44.6b	(*.f64 (/.f64 z (+.f64 (+.f64 t x) y)) (+.f64 x y))
	28.8b	(/.f64 1 (/.f64 (+.f64 x (+.f64 y t)) (fma.f64 y (-.f64 a b) (fma.f64 z (+.f64 x y) (*.f64 a t)))))

Compiler

Compiled 10177 to 3040 computations (70.1% saved)

regimes2.6s (37.9%)

Accuracy

Total 4.3b remaining (57.6%)

Threshold costs 0b (0%)

Counts

96 → 3

Compiler

Compiled 19829 to 9967 computations (49.7% saved)

bsearch4.0ms (0.1%)

Compiler: Compiled 27 to 16 computations (40.7% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

13×	`+-commutative_binary64`
7×	`*-commutative_binary64`
6×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	108
1	54	108
2	67	108
3	73	108
4	76	108
5	76	108

end1.0ms (0%)

Compiler: Compiled 79 to 31 computations (60.8% saved)

sample1.0s (15.1%)

Algorithm

1×

intervals

Results

526.0ms	7998×	body	128	valid
0.0ms	1×	body	1024	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 578 to 294 computations (49.1% saved)

Details

analyze1.9s (27.6%)

sample33.0ms (0.5%)

simplify94.0ms (1.4%)

prune3.0ms (0%)

localize13.0ms (0.2%)

series182.0ms (2.6%)

rewrite13.0ms (0.2%)

simplify157.0ms (2.3%)

prune174.0ms (2.5%)

localize3.0ms (0.1%)

series5.0ms (0.1%)

rewrite7.0ms (0.1%)

simplify74.0ms (1.1%)

prune47.0ms (0.7%)

localize3.0ms (0.1%)

prune18.0ms (0.3%)

localize13.0ms (0.2%)

series186.0ms (2.7%)

rewrite11.0ms (0.2%)

simplify155.0ms (2.2%)

prune136.0ms (2%)

regimes2.6s (37.9%)

bsearch4.0ms (0.1%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.0s (15.1%)

Profiling