Details

sample201.0ms

Algorithm

intervals

Results

68.0ms	1412×	body	80	nan
33.0ms	509×	body	80	valid

simplify64.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

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

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- t 1.0) (log a))
0.2b	(* y (log z))
1.1b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
1.3b	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

rewrite288.0ms

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:

22.0ms	(* (- t 1.0) (log a))
9.0ms	(* y (log z))
75.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
179.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

series409.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (- t 1.0) (log a))
38.0ms	(* y (log z))
121.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
184.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

simplify72.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (60.0ms)

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

prune479.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

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))
0.2b	(fma (log (/ 1 a)) t b)
1.3b	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

rewrite87.0ms

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:

54.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))
0.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
0.0ms	(fma (log (/ 1 a)) t b)
24.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

series1.2s

Counts

4 → 12

Calls

4 calls:

617.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))
90.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
86.0ms	(fma (log (/ 1 a)) t b)
356.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

simplify108.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 2 (86.0ms)

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

prune805.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize26.0ms

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))
0.2b	(fma (log (/ 1 a)) t b)
1.4b	(* (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) (/ 1 y))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

120×	`times-frac`
118×	`add-exp-log`
85×	`associate-r`
79×	`add-sqr-sqrt`
67×	`prod-exp`
63×	`*-un-lft-identity`
62×	`add-cube-cbrt`
56×	`div-exp`
55×	`unpow-prod-down`
30×	`add-cbrt-cube`
20×	`pow-exp`
19×	`fma-udef`
17×	`exp-sum`
13×	`rec-exp` `1-exp`
12×	`cbrt-unprod`
11×	`pow1`
6×	`cbrt-undiv` `div-inv` `unswap-sqr`
5×	`pow-to-exp` `sqr-pow`
4×	`expm1-log1p-u` `associate-r/` `associate-l*` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative`
1×	`frac-times` `associate-*l/` `un-div-inv`

Counts

4 → 190

Calls

4 calls:

52.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))
0.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
0.0ms	(fma (log (/ 1 a)) t b)
77.0ms	(* (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) (/ 1 y))

series892.0ms

Counts

4 → 12

Calls

4 calls:

369.0ms	(* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))
86.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
83.0ms	(fma (log (/ 1 a)) t b)
353.0ms	(* (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) (/ 1 y))

simplify59.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1118	2775
1	5001	2428

prune881.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (log (/ 1 a)) t b)
0.2b	(fma (log (/ 1 a)) t b)
0.2b	(fma (log (/ 1 a)) t b)
1.4b	(* (* (* x (/ (pow (/ 1 a) (/ 1.0 2)) (* (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))))) (/ (pow (/ 1 a) (/ 1.0 2)) (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) (/ 1 y))

rewrite543.0ms

Algorithm

rewrite-expression-head

Rules

2491×	`add-exp-log`
1320×	`prod-exp`
1094×	`div-exp`
448×	`pow-exp`
211×	`rec-exp` `1-exp`
112×	`pow-to-exp`
81×	`add-cbrt-cube`
50×	`cbrt-unprod`
25×	`cbrt-undiv`
13×	`pow1` `associate-r`
11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`associate-*r/`
6×	`pow-prod-down`
5×	`frac-times` `associate-*l/`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef`
1×	`associate-l` `un-div-inv` `*-commutative` `div-inv`

Counts

4 → 479

Calls

4 calls:

0.0ms	(fma (log (/ 1 a)) t b)
0.0ms	(fma (log (/ 1 a)) t b)
0.0ms	(fma (log (/ 1 a)) t b)
471.0ms	(* (* (* x (/ (pow (/ 1 a) (/ 1.0 2)) (* (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))))) (/ (pow (/ 1 a) (/ 1.0 2)) (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) (/ 1 y))

series599.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(fma (log (/ 1 a)) t b)
77.0ms	(fma (log (/ 1 a)) t b)
80.0ms	(fma (log (/ 1 a)) t b)
358.0ms	(* (* (* x (/ (pow (/ 1 a) (/ 1.0 2)) (* (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))) (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))))) (/ (pow (/ 1 a) (/ 1.0 2)) (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b)))))) (/ 1 y))

simplify196.0ms

Algorithm

egg-herbie

Counts

491 → 491

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	2391	16620
1	5002	14685

prune565.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes389.0ms

Accuracy

92.1% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 1.3b

bsearch366.0ms

Steps

Iters	Range		Point
8	322852495373993.94	1.0902156719045573e+17	717450678909797.0
9	-23694.980629839803	-0.10423345619917944	-1015.9319810348419

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	52	77
1	52	77

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.3s	46186×	body	80	nan
920.0ms	15239×	body	80	valid