Details

analyze3.5s

Algorithm

sampling

Space saved by range analysis: 0.195169%

Space saved by search: 21.247751%

Guaranteed chance to sample good point: 32.766089%

sample92.0ms

Algorithm

intervals

Results

27.0ms	44×	body	1280	valid
22.0ms	47×	body	640	valid
8.0ms	114×	body	80	valid
6.0ms	30×	body	320	valid
3.0ms	3×	body	2560	valid
2.0ms	18×	body	160	valid
2.0ms	6×	body	640	nan
1.0ms	22×	body	80	nan
1.0ms	14×	body	80	overflowed
1.0ms	4×	body	320	nan
1.0ms	2×	body	1280	nan
0.0ms	4×	body	160	nan

simplify220.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	7
1	33	7
2	49	7
3	71	7
4	93	7
5	180	7
6	232	7
7	411	7
8	628	7
9	935	7
10	1028	7
11	1354	7
12	3968	7
13	5002	7

prune4.0ms

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: 26.2b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (exp z))
0.1b	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
2.1b	(log (+ (- 1.0 y) (* y (exp z))))
4.5b	(+ (- 1.0 y) (* y (exp z)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
11×	`pow1`
9×	`add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
5×	`log-pow`
4×	`log-div` `associate-/l*`
3×	`log-prod` `flip3-+` `associate-r` `associate-l` `associate-/r*` `flip-+`
2×	`associate-+l+` `div-sub` `sum-log`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

5.0ms	(* y (exp z))
8.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
5.0ms	(log (+ (- 1.0 y) (* y (exp z))))
6.0ms	(+ (- 1.0 y) (* y (exp z)))

series70.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(* y (exp z))
44.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
14.0ms	(log (+ (- 1.0 y) (* y (exp z))))
7.0ms	(+ (- 1.0 y) (* y (exp z)))

simplify51.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	452	795
1	1740	733
2	5002	726

prune185.0ms

Filtered

68 candidates to 92 candidates (-35.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	84	8	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	8	93

Merged error: 4.7b

Counts

93 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 0.5 (pow z 2)) (* 1.0 z))
0.0b	(- x (/ (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) t))
4.1b	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
5.7b	(/ (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) t)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
14×	`add-cube-cbrt`
10×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1`
3×	`flip3-+` `associate-r` `associate-l` `associate-/r` `flip-+` `associate-/l`
2×	`associate-*r/` `associate-/l/` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `sub-neg` `flip3--` `frac-2neg` `distribute-lft-in` `diff-log` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 77

Calls

4 calls:

4.0ms	(+ (* 0.5 (pow z 2)) (* 1.0 z))
8.0ms	(- x (/ (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) t))
7.0ms	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
6.0ms	(/ (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) t)

series78.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (* 0.5 (pow z 2)) (* 1.0 z))
35.0ms	(- x (/ (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) t))
14.0ms	(* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))
23.0ms	(/ (+ (log 1.0) (* y (+ (* 0.5 (pow z 2)) (* 1.0 z)))) t)

simplify52.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	402	953
1	1641	882
2	5001	876

prune236.0ms

Filtered

66 candidates to 89 candidates (-34.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	82	7	89
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	83	14	97

Merged error: 4.6b

Counts

97 → 14

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(- x (+ (* 1.0 (/ (* z y) t)) (/ (log 1.0) t)))
4.5b	(/ (* z y) t)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`add-sqr-sqrt` `*-un-lft-identity`
4×	`add-cube-cbrt`
3×	`times-frac` `associate-/r*`
2×	`pow1` `cbrt-undiv` `diff-log` `div-exp`
1×	`sub-neg` `flip3--` `frac-2neg` `prod-exp` `clear-num` `sum-log` `flip--` `cbrt-unprod` `div-inv` `associate-/l*` `associate--r+` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 37

Calls

2 calls:

11.0ms	(- x (+ (* 1.0 (/ (* z y) t)) (/ (log 1.0) t)))
4.0ms	(/ (* z y) t)

series24.0ms

Counts

2 → 6

Calls

2 calls:

19.0ms	(- x (+ (* 1.0 (/ (* z y) t)) (/ (log 1.0) t)))
5.0ms	(/ (* z y) t)

simplify79.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	204	286
1	812	256
2	3760	256
3	5001	256

prune123.0ms

Filtered

29 candidates to 43 candidates (-48.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	35	8	43
Fresh	6	7	13
Picked	1	0	1
Done	0	0	0
Total	42	15	57

Merged error: 4.0b

Counts

57 → 15

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(- x (+ (* 1.0 (* z (/ y t))) (/ (log 1.0) t)))
4.9b	(* z (/ y t))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`associate-r`
12×	`*-un-lft-identity`
10×	`add-cube-cbrt` `times-frac`
7×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1`
3×	`associate-l`
2×	`diff-log` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `flip3--` `associate-r/` `div-exp` `pow-prod-down` `sum-log` `-commutative` `flip--` `div-inv` `associate--r+` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 48

Calls

2 calls:

11.0ms	(- x (+ (* 1.0 (* z (/ y t))) (/ (log 1.0) t)))
7.0ms	(* z (/ y t))

series22.0ms

Counts

2 → 6

Calls

2 calls:

17.0ms	(- x (+ (* 1.0 (* z (/ y t))) (/ (log 1.0) t)))
5.0ms	(* z (/ y t))

simplify104.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	272	334
1	1124	304
2	4767	304
3	5002	304

prune67.0ms

Filtered

36 candidates to 54 candidates (-50.0%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	51	3	54
Fresh	2	12	14
Picked	0	1	1
Done	0	0	0
Total	53	16	69

Merged error: 4.0b

Counts

69 → 16

Details

analyze3.5s

sample92.0ms

simplify220.0ms

prune4.0ms

localize11.0ms

rewrite26.0ms

series70.0ms

simplify51.0ms

prune185.0ms

localize16.0ms

rewrite27.0ms

series78.0ms

simplify52.0ms

prune236.0ms

localize10.0ms

rewrite16.0ms

series24.0ms

simplify79.0ms

prune123.0ms

localize10.0ms

rewrite19.0ms

series22.0ms

simplify104.0ms

prune67.0ms

regimes1.2s

bsearch2.0ms

Profiling