Details

sample176.0ms

Algorithm

intervals

Results

70.0ms	1402×	body	80	nan
32.0ms	495×	body	80	valid

simplify55.0ms

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

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:

0.1b	(* (- t 1.0) (log a))
0.3b	(* y (log z))
1.0b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
1.4b	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

395×	`*-un-lft-identity`
215×	`exp-sum`
192×	`associate-r`
177×	`add-sqr-sqrt`
165×	`times-frac`
161×	`add-cube-cbrt`
135×	`prod-diff`
132×	`associate-l`
96×	`distribute-lft-out`
72×	`log-prod`
70×	`associate--l+`
55×	`associate-/l*`
40×	`distribute-lft-out--`
36×	`distribute-rgt-in` `distribute-lft-in`
30×	`associate-+l+` `associate-+r+`
15×	`add-exp-log`
13×	`add-cbrt-cube`
11×	`exp-prod`
10×	`pow1` `add-log-exp`
6×	`*-commutative` `unswap-sqr`
5×	`+-commutative` `sub-neg`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u`
3×	`div-exp` `associate-/r*` `cbrt-unprod` `rem-exp-log`
2×	`cbrt-undiv` `exp-diff` `diff-log` `pow-prod-down` `associate-*l/` `log-pow` `difference-of-squares`
1×	`flip3--` `frac-2neg` `associate-*r/` `clear-num` `sum-log` `flip--` `div-inv` `associate-/l/`

Counts

4 → 366

Calls

4 calls:

7.0ms	(* (- t 1.0) (log a))
5.0ms	(* y (log z))
30.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
55.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

series431.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (- t 1.0) (log a))
39.0ms	(* y (log z))
120.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
184.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

simplify140.0ms

Algorithm

egg-herbie

Counts

378 → 378

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1287	5547
1	4881	4154
2	5001	4154

prune687.0ms

Filtered

378 candidates to 185 candidates (48.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	373	5	378
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	375	5	380

Merged error: 0.0b

Counts

380 → 5

localize22.0ms

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)
0.2b	(/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (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))))) y)

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

824×	`times-frac`
434×	`add-sqr-sqrt`
371×	`*-un-lft-identity`
366×	`add-cube-cbrt`
298×	`unpow-prod-down`
288×	`associate-r`
121×	`associate-/l*`
89×	`fma-udef`
87×	`exp-sum`
69×	`add-exp-log`
46×	`div-exp`
28×	`div-inv`
26×	`associate-/l/` `sqr-pow`
24×	`associate-*r/` `unswap-sqr`
16×	`pow-exp`
15×	`add-cbrt-cube`
13×	`prod-exp`
12×	`associate-l`
11×	`associate-/r*`
5×	`cbrt-undiv`
4×	`pow1` `expm1-log1p-u` `pow-to-exp` `rec-exp` `1-exp` `clear-num` `*-commutative` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg`
2×	`un-div-inv` `cbrt-unprod`

Counts

4 → 536

Calls

4 calls:

1.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
1.0ms	(fma (log (/ 1 a)) t b)
15.0ms	(/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))
47.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

series853.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))
85.0ms	(fma (log (/ 1 a)) t b)
316.0ms	(/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))
362.0ms	(/ (* x (/ (pow (/ 1 a) 1.0) (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y)

simplify156.0ms

Algorithm

egg-herbie

Counts

548 → 548

Iterations

Useful iterations: 1 (47.0ms)

Iter	Nodes	Cost
0	2611	10969
1	5001	10622

prune2.1s

Filtered

548 candidates to 392 candidates (71.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	546	2	548
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	548	5	553

Merged error: 0.0b

Counts

553 → 5

localize35.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
0.6b	(cbrt y)
1.0b	(* (/ (* x (/ (pow (/ (* (cbrt 1) (cbrt 1)) 1) 1.0) (* (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))))))) (* (cbrt y) (cbrt y))) (/ (/ (pow (/ (cbrt 1) a) 1.0) (cbrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) (cbrt y)))

rewrite9.9m

Algorithm: rewrite-expression-head