Details

analyze1.3s (26.3%)

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
5.8%	93.9%	0.3%	11
8.4%	91.3%	0.3%	12
9.7%	90%	0.3%	13
10.7%	89%	0.3%	14

sample59.0ms (1.2%)

Algorithm

1×

intervals

Results

31.0ms	256×	body	80	valid
1.0ms	6×	body	80	invalid

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	46	17
1	46	17

prune18.0ms (0.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 14.0b

Counts

2 → 1

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+ x (/ (* y z) t))
6.1b	(/ (* y b) t)
6.9b	(/ (* y z) t)
9.1b	(/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))

rewrite29.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`*-un-lft-identity`
26×	`times-frac`
22×	`distribute-lft-out`
19×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/r*`
6×	`associate-/l*` `add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`pow1` `flip3-+` `associate-/r/` `flip-+`
3×	`frac-2neg` `clear-num` `div-inv`
2×	`frac-add` `prod-exp` `cbrt-unprod` `associate-/l/`
1×	`+-commutative` `sum-log`

Counts

4 → 101

Calls

4 calls:

13.0ms	(/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))
4.0ms	(+ x (/ (* y z) t))
4.0ms	(/ (* y z) t)
4.0ms	(/ (* y b) t)

series58.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))
8.0ms	(+ x (/ (* y z) t))
5.0ms	(/ (* y z) t)
5.0ms	(/ (* y b) t)

simplify41.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5082	1595

prune240.0ms (4.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	98	15	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	99	15	114

Merged error: 8.7b

Counts

114 → 15

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.3b	(/ (* (/ y (* (cbrt t) (cbrt t))) z) (cbrt t))
3.7b	(* (/ y (* (cbrt t) (cbrt t))) z)
6.1b	(/ (* y b) t)
9.1b	(/ (+ x (/ (* (/ y (* (cbrt t) (cbrt t))) z) (cbrt t))) (+ (+ a 1.0) (/ (* y b) t)))

rewrite40.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`*-un-lft-identity`
34×	`add-exp-log`
33×	`times-frac`
28×	`add-sqr-sqrt`
26×	`add-cbrt-cube`
24×	`add-cube-cbrt`
21×	`distribute-lft-out`
14×	`associate-/r*`
11×	`cbrt-undiv` `div-exp`
9×	`prod-exp` `cbrt-unprod`
7×	`associate-l`
6×	`pow1` `cbrt-prod` `associate-/l*`
4×	`associate-/r/` `div-inv` `add-log-exp`
3×	`frac-2neg` `flip3-+` `associate-r` `clear-num` `flip-+` `associate-/l/`
2×	`associate-*l/` `frac-add` `unswap-sqr`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 128

Calls

4 calls:

14.0ms	(/ (+ x (/ (* (/ y (* (cbrt t) (cbrt t))) z) (cbrt t))) (+ (+ a 1.0) (/ (* y b) t)))
9.0ms	(/ (* (/ y (* (cbrt t) (cbrt t))) z) (cbrt t))
8.0ms	(* (/ y (* (cbrt t) (cbrt t))) z)
4.0ms	(/ (* y b) t)

series116.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ (+ x (/ (* (/ y (* (cbrt t) (cbrt t))) z) (cbrt t))) (+ (+ a 1.0) (/ (* y b) t)))
34.0ms	(* (/ y (* (cbrt t) (cbrt t))) z)
10.0ms	(/ (* (/ y (* (cbrt t) (cbrt t))) z) (cbrt t))
5.0ms	(/ (* y b) t)

simplify34.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5380	1922

prune461.0ms (9.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	136	4	140
Fresh	4	10	14
Picked	1	0	1
Done	0	0	0
Total	141	14	155

Merged error: 8.2b

Counts

155 → 14

localize20.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.3b	(/ (* (/ y (* (cbrt t) (cbrt t))) z) (cbrt t))
2.8b	(* (/ y (* (cbrt t) (cbrt t))) (/ b (cbrt t)))
3.7b	(* (/ y (* (cbrt t) (cbrt t))) z)
9.1b	(/ (+ x (/ (* (/ y (* (cbrt t) (cbrt t))) z) (cbrt t))) (+ (+ a 1.0) (* (/ y (* (cbrt t) (cbrt t))) (/ b (cbrt t)))))

rewrite50.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
50×	`add-exp-log` `times-frac`
43×	`*-un-lft-identity`
35×	`add-cube-cbrt` `add-cbrt-cube`
25×	`associate-r`
17×	`cbrt-prod`
16×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
14×	`associate-l`
9×	`associate-/r*`
8×	`pow1` `associate-/r/` `unswap-sqr`
6×	`frac-add`
5×	`flip3-+` `associate-l/` `flip-+` `div-inv` `associate-/l`
4×	`distribute-lft-out` `add-log-exp`
3×	`frac-times` `associate-*r/` `associate-/l/`
2×	`frac-2neg` `pow-prod-down` `clear-num` `*-commutative`

Counts

4 → 160

Calls

4 calls:

14.0ms	(* (/ y (* (cbrt t) (cbrt t))) (/ b (cbrt t)))
13.0ms	(/ (+ x (/ (* (/ y (* (cbrt t) (cbrt t))) z) (cbrt t))) (+ (+ a 1.0) (* (/ y (* (cbrt t) (cbrt t))) (/ b (cbrt t)))))
9.0ms	(/ (* (/ y (* (cbrt t) (cbrt t))) z) (cbrt t))
8.0ms	(* (/ y (* (cbrt t) (cbrt t))) z)

series126.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

72.0ms	(/ (+ x (/ (* (/ y (* (cbrt t) (cbrt t))) z) (cbrt t))) (+ (+ a 1.0) (* (/ y (* (cbrt t) (cbrt t))) (/ b (cbrt t)))))
32.0ms	(* (/ y (* (cbrt t) (cbrt t))) z)
11.0ms	(* (/ y (* (cbrt t) (cbrt t))) (/ b (cbrt t)))
10.0ms	(/ (* (/ y (* (cbrt t) (cbrt t))) z) (cbrt t))

simplify41.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5228	2410

prune298.0ms (6.1%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	170	2	172
Fresh	2	11	13
Picked	0	1	1
Done	0	0	0
Total	172	14	186

Merged error: 8.2b

Counts

186 → 14

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+ x (* (/ y t) z))
4.8b	(* (/ y t) z)
6.1b	(/ (* y b) t)
9.1b	(/ (+ x (* (/ y t) z)) (+ (+ a 1.0) (/ (* y b) t)))

rewrite27.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`*-un-lft-identity`
29×	`add-sqr-sqrt`
28×	`times-frac`
24×	`add-cube-cbrt`
16×	`add-exp-log` `add-cbrt-cube`
13×	`associate-l`
12×	`distribute-lft-out`
8×	`associate-/r*`
6×	`pow1` `add-log-exp`
4×	`cbrt-undiv` `flip3-+` `div-exp` `associate-/r/` `flip-+` `associate-/l*`
3×	`associate-r` `prod-exp` `cbrt-unprod` `div-inv`
2×	`frac-2neg` `frac-add` `clear-num` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `pow-prod-down` `associate-l/` `sum-log` `-commutative`

Counts

4 → 105

Calls

4 calls:

11.0ms	(/ (+ x (* (/ y t) z)) (+ (+ a 1.0) (/ (* y b) t)))
6.0ms	(* (/ y t) z)
4.0ms	(/ (* y b) t)
3.0ms	(+ x (* (/ y t) z))

series82.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ (+ x (* (/ y t) z)) (+ (+ a 1.0) (/ (* y b) t)))
11.0ms	(+ x (* (/ y t) z))
5.0ms	(* (/ y t) z)
5.0ms	(/ (* y b) t)

simplify28.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5105	1517

prune142.0ms (2.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	115	2	117
Fresh	2	10	12
Picked	1	0	1
Done	1	0	1
Total	119	12	131

Merged error: 8.2b

Counts

131 → 12

regimes805.0ms (16.6%)

Accuracy

Total 3.5b remaining (25.4%)

Threshold costs 0b (0%)

bsearch45.0ms (0.9%)

Steps

Iters	Range		Point
7	6.734230674045045e-140	1.3469265749450483e-138	1.3583837970033708e-139
10	-8.603742217837876e-84	-5.787207828469491e-99	-2.642073336958404e-86

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	144	47
1	144	47

end0.0ms (0%)

sample763.0ms (15.7%)

Algorithm

1×

intervals

Results

448.0ms	8000×	body	80	valid
18.0ms	285×	body	80	invalid

Details

analyze1.3s (26.3%)

sample59.0ms (1.2%)

simplify5.0ms (0.1%)

prune18.0ms (0.4%)

localize14.0ms (0.3%)

rewrite29.0ms (0.6%)

series58.0ms (1.2%)

simplify41.0ms (0.8%)

prune240.0ms (4.9%)

localize16.0ms (0.3%)

rewrite40.0ms (0.8%)

series116.0ms (2.4%)

simplify34.0ms (0.7%)

prune461.0ms (9.5%)

localize20.0ms (0.4%)

rewrite50.0ms (1%)

series126.0ms (2.6%)

simplify41.0ms (0.8%)

prune298.0ms (6.1%)

localize12.0ms (0.3%)

rewrite27.0ms (0.6%)

series82.0ms (1.7%)

simplify28.0ms (0.6%)

prune142.0ms (2.9%)

regimes805.0ms (16.6%)

bsearch45.0ms (0.9%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample763.0ms (15.7%)

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