Details

sample178.0ms

Algorithm

intervals

Results

74.0ms	1396×	body	80	nan
30.0ms	494×	body	80	valid

simplify51.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (4.0ms)

Iter	Nodes	Cost
0	32	10
1	65	10
2	181	8
3	522	8
4	2203	8
5	5002	8

prune10.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 0.2b

Counts

2 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- t 1.0) (log a))
0.3b	(* y (log z))
0.9b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
1.3b	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 95

Calls

4 calls:

7.0ms	(* (- t 1.0) (log a))
4.0ms	(* y (log z))
6.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
11.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

series372.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (- t 1.0) (log a))
40.0ms	(* y (log z))
112.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
167.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

simplify57.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	493	869
1	2033	715
2	5001	683

prune347.0ms

Filtered

107 candidates to 75 candidates (70.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	104	3	107
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	105	4	109

Merged error: 0.0b

Counts

109 → 4

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))
0.3b	(* (log (/ 1 a)) t)
0.3b	(* y (log (/ 1 z)))
4.5b	(/ (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))) (/ y x))

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

3067×	`times-frac`
1238×	`add-sqr-sqrt`
1234×	`add-cube-cbrt` `*-un-lft-identity`
728×	`unpow-prod-down`
239×	`exp-sum`
146×	`div-inv`
72×	`associate-/l*`
56×	`sqr-pow`
43×	`add-exp-log`
37×	`div-exp`
26×	`log-prod`
20×	`add-cbrt-cube`
13×	`distribute-rgt-in` `distribute-lft-in` `associate-/r*`
12×	`pow1`
10×	`add-log-exp`
9×	`associate-r` `associate-l`
8×	`cbrt-undiv` `pow-exp`
6×	`log-pow`
3×	`exp-prod` `sum-log` `rem-exp-log`
2×	`pow-to-exp` `rec-exp` `pow-flip` `1-exp` `log-rec` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `inv-pow` `unswap-sqr`
1×	`distribute-lft-neg-out` `frac-2neg` `clear-num` `associate-/r/` `distribute-rgt-neg-out` `associate-/l/`

Counts

4 → 1135

Calls

4 calls:

8.0ms	(exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))
4.0ms	(* (log (/ 1 a)) t)
7.0ms	(* y (log (/ 1 z)))
46.0ms	(/ (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))) (/ y x))

series726.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))
66.0ms	(* (log (/ 1 a)) t)
38.0ms	(* y (log (/ 1 z)))
534.0ms	(/ (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))) (/ y x))

simplify304.0ms

Algorithm

egg-herbie

Counts

1147 → 1147

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5001	32428

prune5.7s

Filtered

1147 candidates to 878 candidates (76.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	1144	3	1147
Fresh	1	1	2
Picked	0	1	1
Done	1	0	1
Total	1146	5	1151

Merged error: 0b

Counts

1151 → 5

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))
0.3b	(* (log (/ 1 a)) t)
0.3b	(* y (log (/ 1 z)))
1.3b	(* (/ 1 y) (* (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))) x))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

108×	`add-exp-log`
62×	`prod-exp`
48×	`div-exp`
34×	`add-sqr-sqrt`
30×	`add-cube-cbrt` `*-un-lft-identity`
29×	`add-cbrt-cube`
27×	`times-frac`
26×	`log-prod`
22×	`associate-l`
17×	`pow1`
16×	`pow-exp`
13×	`distribute-rgt-in` `distribute-lft-in`
12×	`rec-exp` `1-exp` `cbrt-unprod`
10×	`associate-r` `add-log-exp`
6×	`log-pow`
5×	`cbrt-undiv` `pow-prod-down`
4×	`pow-to-exp`
3×	`exp-prod` `associate-l/` `sum-log` `-commutative` `div-inv` `rem-exp-log`
2×	`pow-flip` `log-rec` `inv-pow` `unswap-sqr`
1×	`distribute-lft-neg-out` `frac-times` `associate-*r/` `exp-sum` `distribute-rgt-neg-out`

Counts

4 → 149

Calls

4 calls:

9.0ms	(exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))
5.0ms	(* (log (/ 1 a)) t)
7.0ms	(* y (log (/ 1 z)))
23.0ms	(* (/ 1 y) (* (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))) x))

series718.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))
66.0ms	(* (log (/ 1 a)) t)
38.0ms	(* y (log (/ 1 z)))
528.0ms	(* (/ 1 y) (* (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))) x))

simplify84.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	820	1888
1	3344	1541
2	5002	1432

prune472.0ms

Filtered

161 candidates to 87 candidates (54.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	160	1	161
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	161	5	166

Merged error: 0b

Counts

166 → 5

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (cbrt 1) (cbrt 1)) (sqrt a))
0.3b	(* (log (/ 1 a)) t)
0.3b	(* y (log (/ 1 z)))
4.3b	(/ (/ y x) (/ (pow (/ (cbrt 1) (sqrt a)) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))

rewrite457.0ms

Algorithm

rewrite-expression-head

Rules

8473×	`times-frac`
3383×	`add-sqr-sqrt`
3379×	`add-cube-cbrt` `*-un-lft-identity`
2240×	`unpow-prod-down`
1014×	`sqrt-prod`
1008×	`cbrt-prod`
616×	`exp-sum`
255×	`div-inv`
186×	`associate-/r*`
56×	`sqr-pow`
38×	`add-exp-log`
27×	`div-exp`
26×	`log-prod`
23×	`add-cbrt-cube`
14×	`associate-/l*`
13×	`distribute-rgt-in` `distribute-lft-in`
12×	`pow1`
10×	`cbrt-undiv`
9×	`associate-r` `associate-l`
6×	`log-pow`
4×	`pow-exp` `add-log-exp`
3×	`prod-exp` `cbrt-unprod`
2×	`pow-to-exp` `pow-flip` `frac-2neg` `log-rec` `pow-prod-down` `clear-num` `*-commutative` `inv-pow` `unswap-sqr`
1×	`distribute-lft-neg-out` `associate-/r/` `distribute-rgt-neg-out` `associate-/l/`

Counts

4 → 2656

Calls

4 calls:

12.0ms	(/ (* (cbrt 1) (cbrt 1)) (sqrt a))
4.0ms	(* (log (/ 1 a)) t)
7.0ms	(* y (log (/ 1 z)))
88.0ms	(/ (/ y x) (/ (pow (/ (cbrt 1) (sqrt a)) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))

series668.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ (* (cbrt 1) (cbrt 1)) (sqrt a))
62.0ms	(* (log (/ 1 a)) t)
39.0ms	(* y (log (/ 1 z)))
539.0ms	(/ (/ y x) (/ (pow (/ (cbrt 1) (sqrt a)) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))

simplify780.0ms

Algorithm

egg-herbie

Counts

2668 → 2668

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5001	92683

prune17.8s

Filtered

2668 candidates to 2026 candidates (75.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	2667	1	2668
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	2668	5	2673

Merged error: 0b

Counts

2673 → 5

regimes267.0ms

Accuracy

90.1% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 1.2b

bsearch342.0ms

Steps

Iters	Range		Point
8	4.167643216640923e-75	5.2558867662888565e-71	1.2266431991864999e-73
10	-1.6483543960726273e-32	-2.3338958226648062e-43	-6.120335577213576e-38

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	29
1	41	29

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.3s	46051×	body	80	nan
937.0ms	15281×	body	80	valid