Details

analyze1.8s (15.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	49.9%	50.1%	0
0%	49.9%	50.1%	1
0%	49.9%	50.1%	2
0%	49.9%	50.1%	3
0%	49.9%	50.1%	4
0%	49.9%	50.1%	5
0%	49.9%	50.1%	6
0%	49.9%	50.1%	7
0%	49.9%	50.1%	8
0.4%	49.5%	50.1%	9
0.4%	49.3%	50.3%	10
0.6%	48.9%	50.5%	11
1.1%	48.1%	50.9%	12
1.5%	47.3%	51.2%	13
1.7%	46.9%	51.5%	14

Compiler

Compiled 31 to 24 computations (22.6% saved)

sample183.0ms (1.7%)

Algorithm

1×

intervals

Results

106.0ms	133×	body	2048	valid
28.0ms	72×	body	1024	valid
7.0ms	14×	body	2048	overflowed
7.0ms	307×	pre	128	true
7.0ms	22×	body	1024	overflowed
6.0ms	25×	body	512	valid
5.0ms	1×	body	4096	valid
1.0ms	9×	body	256	valid
1.0ms	16×	body	128	valid
1.0ms	3×	body	512	overflowed
1.0ms	8×	body	128	overflowed
1.0ms	4×	body	256	overflowed

Compiler

Compiled 55 to 46 computations (16.4% saved)

simplify24.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	5217	37

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 60.2b

Counts

2 → 1

Compiler

Compiled 48 to 38 computations (20.8% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.7b	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
3.2b	(-.f64 (exp.f64 (*.f64 a eps)) 1)
4.2b	(-.f64 (exp.f64 (*.f64 b eps)) 1)
6.0b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

rewrite40.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
15×	`cancel-sign-sub-inv_binary64`
11×	`add-cube-cbrt_binary64`
10×	`add-log-exp_binary64` `difference-of-squares_binary64`
9×	`flip3--_binary64` `flip--_binary64`
7×	`associate-r_binary64` `associate-l_binary64`
6×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`sub-neg_binary64` `difference-of-sqr-1_binary64` `distribute-lft-out--_binary64`
4×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `frac-times_binary64`
3×	`diff-log_binary64`
2×	`associate-r/_binary64` `associate-l/_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 96

Calls

4 calls:

13.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
7.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
5.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
5.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)

series269.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

98.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
82.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
46.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)
43.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)

simplify71.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4999	2058
1	4999	2058

prune204.0ms (1.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	104	4	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	4	109

Merged error: 49.1b

Counts

109 → 4

Compiler

Compiled 4883 to 2432 computations (50.2% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.6b	(.f64 b (.f64 1/6 (pow.f64 eps 3)))
3.2b	(-.f64 (exp.f64 (*.f64 a eps)) 1)
6.0b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
14.6b	(.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (.f64 eps eps))))

rewrite40.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-exp-log_binary64`
17×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64` `add-cbrt-cube_binary64`
11×	`pow1_binary64`
10×	`prod-exp_binary64`
8×	`add-log-exp_binary64` `add-cube-cbrt_binary64`
6×	`cbrt-unprod_binary64` `cancel-sign-sub-inv_binary64`
4×	`pow-prod-down_binary64` `associate-r_binary64` `associate-l_binary64` `difference-of-squares_binary64`
2×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `associate-r/_binary64` `difference-of-sqr-1_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `-commutative_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `flip-+_binary64` `pow-exp_binary64`

Counts

4 → 78

Calls

4 calls:

13.0ms	(.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (.f64 eps eps))))
7.0ms	(.f64 b (.f64 1/6 (pow.f64 eps 3)))
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
5.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)

series394.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

188.0ms	(.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (.f64 eps eps))))
85.0ms	(.f64 b (.f64 1/6 (pow.f64 eps 3)))
74.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
47.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)

simplify78.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4933	1509
1	4933	1509

prune212.0ms (1.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	86	4	90
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	87	7	94

Merged error: 48.5b

Counts

94 → 7

Compiler

Compiled 5499 to 2873 computations (47.8% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.2b	(-.f64 (exp.f64 (*.f64 a eps)) 1)
4.0b	(.f64 b (.f64 b (.f64 (.f64 eps eps) (+.f64 (.f64 (.f64 b 1/6) eps) 1/2))))
6.0b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
8.7b	(.f64 b (.f64 (.f64 eps eps) (+.f64 (.f64 (*.f64 b 1/6) eps) 1/2)))

rewrite56.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
16×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `prod-exp_binary64` `add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
10×	`associate-*r/_binary64`
8×	`add-log-exp_binary64` `add-cube-cbrt_binary64`
6×	`associate-l_binary64` `cancel-sign-sub-inv_binary64`
4×	`difference-of-squares_binary64`
2×	`flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `associate-r_binary64` `difference-of-sqr-1_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

4 → 97

Calls

4 calls:

17.0ms	(.f64 b (.f64 b (.f64 (.f64 eps eps) (+.f64 (.f64 (.f64 b 1/6) eps) 1/2))))
13.0ms	(.f64 b (.f64 (.f64 eps eps) (+.f64 (.f64 (*.f64 b 1/6) eps) 1/2)))
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
5.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)

series407.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

154.0ms	(.f64 b (.f64 b (.f64 (.f64 eps eps) (+.f64 (.f64 (.f64 b 1/6) eps) 1/2))))
137.0ms	(.f64 b (.f64 (.f64 eps eps) (+.f64 (.f64 (*.f64 b 1/6) eps) 1/2)))
74.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
41.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)

simplify46.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5192	2166

prune238.0ms (2.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	105	4	109
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	108	8	116

Merged error: 48.2b

Counts

116 → 8

Compiler

Compiled 6381 to 3340 computations (47.7% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.2b	(+.f64 -1 (exp.f64 (*.f64 eps a)))
4.0b	(.f64 b (.f64 b (.f64 (.f64 eps eps) (+.f64 (.f64 (.f64 b 1/6) eps) 1/2))))
6.0b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
8.7b	(.f64 b (.f64 (.f64 eps eps) (+.f64 (.f64 (*.f64 b 1/6) eps) 1/2)))

rewrite54.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
16×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `prod-exp_binary64`
12×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`associate-*r/_binary64`
8×	`add-log-exp_binary64`
7×	`add-cube-cbrt_binary64`
6×	`associate-l_binary64`
3×	`flip3-+_binary64` `cancel-sign-sub-inv_binary64` `flip-+_binary64`
2×	`associate-r_binary64` `difference-of-squares_binary64` `*-commutative_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `difference-of-sqr-1_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 91

Calls

4 calls:

16.0ms	(.f64 b (.f64 b (.f64 (.f64 eps eps) (+.f64 (.f64 (.f64 b 1/6) eps) 1/2))))
14.0ms	(.f64 b (.f64 (.f64 eps eps) (+.f64 (.f64 (*.f64 b 1/6) eps) 1/2)))
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
4.0ms	(+.f64 -1 (exp.f64 (*.f64 eps a)))

series402.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

147.0ms	(.f64 b (.f64 b (.f64 (.f64 eps eps) (+.f64 (.f64 (.f64 b 1/6) eps) 1/2))))
134.0ms	(.f64 b (.f64 (.f64 eps eps) (+.f64 (.f64 (*.f64 b 1/6) eps) 1/2)))
73.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
47.0ms	(+.f64 -1 (exp.f64 (*.f64 eps a)))

simplify45.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5257	2096

prune177.0ms (1.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	103	8	111

Merged error: 48.2b

Counts

111 → 8

Compiler

Compiled 4666 to 2331 computations (50% saved)

regimes119.0ms (1.1%)

Compiler: Compiled 1056 to 735 computations (30.4% saved)

bsearch167.0ms (1.5%)

Steps

Iters	Range		Point
10	6.27092192293557e+39	1.4961729006054534e+56	8.249043684066252e+42
7	-4602792.950030036	-55555.54354498594	-4497903.061841475

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	80	183
1	80	183

end0.0ms (0%)

sample6.0s (54.1%)

Algorithm

1×

intervals

Results

3.4s	4084×	body	2048	valid
972.0ms	2371×	body	1024	valid
221.0ms	9650×	pre	128	true
188.0ms	592×	body	1024	overflowed
177.0ms	738×	body	512	valid
174.0ms	339×	body	2048	overflowed
59.0ms	293×	body	512	overflowed
40.0ms	267×	body	256	valid
36.0ms	524×	body	128	valid
19.0ms	282×	body	128	overflowed
19.0ms	16×	body	4096	valid
19.0ms	142×	body	256	overflowed
1.0ms	2×	body	2048	invalid

Compiler

Compiled 509 to 339 computations (33.4% saved)

Details

analyze1.8s (15.9%)

sample183.0ms (1.7%)

simplify24.0ms (0.2%)

prune3.0ms (0%)

localize16.0ms (0.1%)

rewrite40.0ms (0.4%)

series269.0ms (2.4%)

simplify71.0ms (0.6%)

prune204.0ms (1.8%)

localize24.0ms (0.2%)

rewrite40.0ms (0.4%)

series394.0ms (3.6%)

simplify78.0ms (0.7%)

prune212.0ms (1.9%)

localize23.0ms (0.2%)

rewrite56.0ms (0.5%)

series407.0ms (3.7%)

simplify46.0ms (0.4%)

prune238.0ms (2.1%)

localize25.0ms (0.2%)

rewrite54.0ms (0.5%)

series402.0ms (3.6%)

simplify45.0ms (0.4%)

prune177.0ms (1.6%)

regimes119.0ms (1.1%)

bsearch167.0ms (1.5%)

simplify3.0ms (0%)

end0.0ms (0%)

sample6.0s (54.1%)

Profiling