Details

sample188.0ms

Algorithm

intervals

Results

80.0ms	1533×	body	80	nan
31.0ms	518×	body	80	valid

simplify52.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	33	10
1	73	10
2	197	8
3	558	8
4	2287	8
5	5001	8

prune9.0ms

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

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- t 1.0) (log a))
0.3b	(* y (log z))
1.0b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
1.0b	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`add-cube-cbrt`
13×	`add-cbrt-cube`
12×	`add-exp-log` `log-prod` `exp-sum`
10×	`pow1` `add-log-exp`
9×	`prod-diff`
8×	`associate-r` `associate-l`
6×	`distribute-rgt-in` `distribute-lft-in`
5×	`exp-prod`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`times-frac` `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 → 112

Calls

4 calls:

7.0ms	(* (- t 1.0) (log a))
5.0ms	(* y (log z))
8.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
12.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

series398.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (- t 1.0) (log a))
40.0ms	(* y (log z))
112.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
194.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

simplify63.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	580	1143
1	2309	897
2	5002	860

prune391.0ms

Filtered

124 candidates to 89 candidates (71.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	121	3	124
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	122	4	126

Merged error: 0.0b

Counts

126 → 4

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))
0.1b	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
0.1b	(fma (log (/ 1 a)) t b)
1.0b	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
74×	`add-sqr-sqrt`
72×	`associate-r`
58×	`*-un-lft-identity`
57×	`add-cube-cbrt`
55×	`unpow-prod-down`
41×	`add-exp-log`
24×	`div-exp`
19×	`fma-udef`
18×	`add-cbrt-cube`
17×	`exp-sum`
14×	`prod-exp`
8×	`pow-exp`
6×	`pow1` `div-inv` `unswap-sqr`
5×	`cbrt-undiv` `sqr-pow`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `associate-/r*`
2×	`pow-to-exp` `rec-exp` `1-exp` `associate-*r/`
1×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `associate-/l/` `associate-/l`

Counts

4 → 153

Calls

4 calls:

22.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))
1.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
1.0ms	(fma (log (/ 1 a)) t b)
18.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

series1.0s

Counts

4 → 12

Calls

4 calls:

529.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))
80.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
68.0ms	(fma (log (/ 1 a)) t b)
343.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

simplify88.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	904	2177
1	4141	1915
2	5001	1905

prune656.0ms

Filtered

165 candidates to 124 candidates (75.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	162	3	165
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	165	4	169

Merged error: 0.0b

Counts

169 → 4

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
0.1b	(fma (log (/ 1 a)) t b)
0.1b	(fma (log (/ 1 a)) t b)
1.0b	(/ (* (/ x (sqrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) (/ (pow (/ 1 a) 1.0) (sqrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) y)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log`
38×	`div-exp`
22×	`add-cbrt-cube`
14×	`prod-exp`
9×	`cbrt-undiv`
8×	`pow-exp`
6×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `associate-/r*` `fma-udef` `associate-/l/`
2×	`pow-to-exp` `rec-exp` `1-exp`
1×	`frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 72

Calls

4 calls:

1.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
1.0ms	(fma (log (/ 1 a)) t b)
1.0ms	(fma (log (/ 1 a)) t b)
22.0ms	(/ (* (/ x (sqrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) (/ (pow (/ 1 a) 1.0) (sqrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) y)

series590.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
71.0ms	(fma (log (/ 1 a)) t b)
70.0ms	(fma (log (/ 1 a)) t b)
344.0ms	(/ (* (/ x (sqrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) (/ (pow (/ 1 a) 1.0) (sqrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) y)

simplify63.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	535	1430
1	2072	1166
2	5002	1137

prune358.0ms

Filtered

84 candidates to 59 candidates (70.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	84	4	88

Merged error: 0.0b

Counts

88 → 4

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) y)
0.1b	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
0.1b	(fma (log (/ 1 a)) t b)
1.9b	(* x (/ (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) y))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

1173×	`times-frac`
526×	`add-sqr-sqrt`
502×	`*-un-lft-identity`
501×	`add-cube-cbrt`
367×	`unpow-prod-down`
220×	`associate-r`
121×	`fma-udef`
119×	`exp-sum`
72×	`associate-/l*`
41×	`add-exp-log`
37×	`div-inv`
30×	`div-exp`
29×	`sqr-pow`
18×	`add-cbrt-cube`
8×	`pow-exp` `prod-exp`
7×	`unswap-sqr`
6×	`pow1` `cbrt-undiv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `associate-/r*` `cbrt-unprod`
2×	`pow-to-exp` `rec-exp` `1-exp`
1×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `associate-/l/`

Counts

4 → 586

Calls

4 calls:

26.0ms	(/ (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) y)
1.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
1.0ms	(fma (log (/ 1 a)) t b)
61.0ms	(* x (/ (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) y))

series778.0ms

Counts

4 → 12

Calls

4 calls:

297.0ms	(/ (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) y)
76.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
70.0ms	(fma (log (/ 1 a)) t b)
334.0ms	(* x (/ (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) y))

simplify134.0ms

Algorithm

egg-herbie

Counts

598 → 598

Iterations

Useful iterations: 1 (40.0ms)

Iter	Nodes	Cost
0	2440	10914
1	5001	10493

prune2.6s

Filtered

598 candidates to 448 candidates (74.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	597	1	598
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	598	4	602

Merged error: 0b

Counts

602 → 4

regimes180.0ms

Accuracy

0% (1.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	22
1	24	22

end0.0ms

sample5.6s

Algorithm

intervals

Results

2.4s	45873×	body	80	nan
968.0ms	15254×	body	80	valid